Problem Statement

You are given a real number X.Y, where Y is a single digit.

Print the following: (quotes for clarity)

• X-, if 0 \leq Y \leq 2;
• X, if 3 \leq Y \leq 6;
• X+, if 7 \leq Y \leq 9.

Constraints

• 1 \leq X \leq 15
• 0 \leq Y \leq 9
• X and Y are integers.

Sample Input 1

15.8

Sample Output 1

15+

Here, printing 15 + will not be accepted: do not print a space between X and +, or between X and -.

Sample Input 2

1.0

Sample Output 2

1-

You will not get inputs such as 1.00 and 1.

Sample Input 3

12.5

Sample Output 3

12

Problem Statement

Takahashi had his N-th birthday, when he was T centimeters tall.
Additionally, we know the following facts:

• In each year between Takahashi's birth (0-th birthday) and his X-th birthday, his height increased by D centimeters. More formally, for each i = 1, 2, \ldots, X, his height increased by D centimeters between his (i-1)-th birthday and his i-th birthday.
• Between Takahashi's X-th birthday and his N-th birthday, his height did not change.

Find Takahashi's height on his M-th birthday, in centimeters.

Constraints

• 0 \leq M \lt N \leq 100
• 1 \leq X \leq N
• 1 \leq T \leq 200
• 1 \leq D \leq 100
• Takahashi was at least 1 centimeter tall at his birth.
• All values in input are integers.

Sample Input 1

38 20 17 168 3

Sample Output 1

168

In this sample, Takahashi was 168 centimeters tall on his 38-th birthday. Also, his height did not change between his 17-th birthday and 38-th birthday.
From these facts, we find that he was 168 centimeters tall on his 20-th birthday, so the answer is 168.

Sample Input 2

1 0 1 3 2

Sample Output 2

1

In this sample, Takahashi was 1 centimeter tall on his 0(=M)-th birthday and 3(=T) centimeters tall on his 1(=N)-st birthday.

Sample Input 3

100 10 100 180 1

Sample Output 3

90

Problem Statement

There are N people numbered Person 1, Person 2, \dots, and Person N. Person i has a family name s_i and a given name t_i.

Consider giving a nickname to each of the N people. Person i's nickname a_i should satisfy all the conditions below.

• a_i coincides with Person i's family name or given name. In other words, a_i = s_i and/or a_i = t_i holds.
• a_i does not coincide with the family name and the given name of any other person. In other words, for all integer j such that 1 \leq j \leq N and i \neq j, it holds that a_i \neq s_j and a_i \neq t_j.

Is it possible to give nicknames to all the N people? If it is possible, print Yes; otherwise, print No.

Constraints

• 2 \leq N \leq 100
• N is an integer.
• s_i and t_i are strings of lengths between 1 and 10 (inclusive) consisting of lowercase English alphabets.

Sample Input 1

3
tanaka taro
tanaka jiro
suzuki hanako

Sample Output 1

Yes

The following assignment satisfies the conditions of nicknames described in the Problem Statement: a_1 = taro, a_2 = jiro, a_3 = hanako. (a_3 may be suzuki, too.)
However, note that we cannot let a_1 = tanaka, which violates the second condition of nicknames, since Person 2's family name s_2 is tanaka too.

Sample Input 2

3
aaa bbb
xxx aaa
bbb yyy

Sample Output 2

No

There is no way to give nicknames satisfying the conditions in the Problem Statement.

Sample Input 3

2
tanaka taro
tanaka taro

Sample Output 3

No

There may be a pair of people with the same family name and the same given name.

Sample Input 4

3
takahashi chokudai
aoki kensho
snu ke

Sample Output 4

Yes

We can let a_1 = chokudai, a_2 = kensho, and a_3 = ke.

Problem Statement

You are given a string S of length N consisting of lowercase English letters. The x-th (1 \le x \le N) character of S is S_x.

For each i=1,2,\dots,N-1, find the maximum non-negative integer l that satisfies all of the following conditions:

• l+i \le N, and
• for all integers k such that 1 \le k \le l, it holds that S_{k} \neq S_{k+i}.

Note that l=0 always satisfies the conditions.

Constraints

• N is an integer such that 2 \le N \le 5000.
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

6
abcbac

Sample Output 1

5
1
2
0
1

In this input, S= abcbac.

• When i=1, we have S_1 \neq S_2, S_2 \neq S_3, \dots, and S_5 \neq S_6, so the maximum value is l=5.
• When i=2, we have S_1 \neq S_3 but S_2 = S_4, so the maximum value is l=1.
• When i=3, we have S_1 \neq S_4 and S_2 \neq S_5 but S_3 = S_6, so the maximum value is l=2.
• When i=4, we have S_1 = S_5, so the maximum value is l=0.
• When i=5, we have S_1 \neq S_6, so the maximum value is l=1.

Problem Statement

Takahashi and Aoki will play the following game against each other.

Starting from Takahashi, the two alternatingly declare an integer between 1 and 2N+1 (inclusive) until the game ends. Any integer declared by either player cannot be declared by either player again. The player who is no longer able to declare an integer loses; the player who didn't lose wins.

In this game, Takahashi will always win. Your task is to actually play the game on behalf of Takahashi and win the game.

Constraints

• 1 \leq N \leq 1000
• N is an integer.

Input and Output

This task is an interactive task (in which your program and the judge program interact with each other via inputs and outputs).
Your program plays the game on behalf of Takahashi, and the judge program plays the game on behalf of Aoki.

First, your program is given a positive integer N from Standard Input. Then, the following procedures are repeated until the game ends.

1. Your program outputs an integer between 1 and 2N+1 (inclusive) to Standard Output, which defines the integer that Takahashi declares. (You cannot output an integer that is already declared by either player.)
2. The integer that Aoki declares is given by the judge program to your program from Standard Input. (No integer that is already declared by either player will be given.) If Aoki has no more integer to declare, 0 is given instead, which means that the game ended and Takahashi won.

Notes

• After each output, you must flush Standard Output. Otherwise, you may get TLE.
• After the game ended and Takahashi won, the program must be terminated immediately. Otherwise, the judge does not necessarily give AC.
• If your program outputs something that violates the rules of the game (such as an integer that has already been declared by either player), your answer is considered incorrect. In such case, the verdict is indeterminate. It does not necessarily give WA.

Sample Input and Output